I'm going to throw my oar into this debate only to give
my idea of "Sighs:"
All or part of it should be animated, if only a part then the two most important parts of it should be included:
- Where the cat came from, why and how it talked, and how it became a part of Kyon's household.
- The crucial character interactions of Kyon and Haruhi: what led up to and why Kyon came this close to doing something completely out of character (and how Itsuki saved the world as we know it).